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Petrakis, Minos Aristidu 2014-12-16T06:18:18Z 2014-12-16T06:18:18Z 10000-01-01 1987 1987 In this thesis we introduce the class (DELTA)(X,Y) of nearly represent- able operators from a Banach space X to a Banach space Y. These are the operators that map X-valued uniformly bounded martingales that are Cauchy in the Pettis norm into Y-valued martingales that converge almost everywhere. We will see that (DELTA)(L('1),X) contains all representable operators and is contained in the class of Dunford-Pettis operators from L('1) to X. We prove that these inclusions are strict in the case X is the space c(,0). We also prove every nearly representable operator from L('1) to a Banach lattice not containing a copy of c(,0) is representable. We study the class of M(,0)-continuous operators. (An operator T : L('1) (--->) X is called M(,0)-continuous if (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI) where the supremum is taken over all subintervals I of 0,1 ). In the last chapter we give geometric conditions on a Banach space X that imply that all operators from L('1) to X are Dunford-Pettis. Made available in DSpace on 2014-12-16T06:18:18Z (GMT). No. of bitstreams: 1 8711851.pdf: 2575739 bytes, checksum: e8f5ca441db6ed229c2c90f27e83c074 (MD5) Previous issue date: 1987 Embargo set by: Seth Robbins for item 71417 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs U of I Only 93 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1987. http://hdl.handle.net/2142/71251 (UMI)AAI8711851 Mathematics Nearly Representable Operators (dunford-Pettis, Radon-Nikodym) text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.